When citta in the Patañjali Yoga Sūtras is translated into English as attention, the connotations of that simple word make the sūtras defining dhāraṇā, dhyāna, and samādhi easier to understand.
dhāraṇā
deśa-bandhaḥ cittasya dhāraṇā - 3.1 PYS
location-binding of attention - dhāraṇā
Binding one's attention to a location - dhāraṇā
(Initially, this binding must last for 12 seconds for attention to be termed dhāraṇā)
What is location?
Location could be in space.
E.g., generally the object of attention is somewhere with respect to your body - outside it, upon it, inside it. It could be the entire body too, but that is more difficult. So generally a small object in space.
Location could be in time.
E.g., we think or plan or give attention to the future. Or worry about it. In the other direction, nostalgia is paying attention to the past. So is regret, or guilt. Again, generally a single event or a set of small events that can be held easily in working memory.
But there is a little-understood subtlety for both location and time. The entire attention or attending activity happens in the mind-field and in the present. We only work with our mental images or our memories of them. Even if the location is just a foot away, my attention does not go out of my body or brain and plop down on that location.
Remember the story of Gaṇeśa and Kārtikeya competing to go around the world and Gaṇeśa wins the prize by going around Śiva and Pārvati - his representations of jagat?
This is what happens with attention, whether it is upon an outside sensation or an internal, mental, event. In both cases, attention works on their internal mental representations or encoding.
Reflex or subconscious actions, while very fast and not analyses, are still the results of outside triggers and due to a circuit from sensory to motor neurons.
Location could be an abstract idea or a vision. Attention even on those occurs with an implicit, underlying, basis of space (inside my mind or brain) and time (thinking today, right now).
Location could be anything, really.
Emotions or feelings, a mental state.
Or physical activities.
Drinking tea.
Eating a sweet.
The generality of this sūtra is amazing. From this, one can get to obsession, positive or negative. That is simply attention resting or stuck involuntarily somewhere, or on someone, or something, for 12 or more seconds, and thus dhāraṇā.
Attention can also be grabbed by something striking or unusual. This is the idea behind advertisements which try to stand out from the normal. Please note that these are outside and also that they try to induce dhāraṇā, by trying to hold your attention for 12 seconds, if not longer!
dhyāna
tatra pratyaya-ekatānatā dhyānam 3.2 PYS
That [attention-binding resulting in] cognition-monotony - dhyānam.
That [attention-binding resulting in a] single-unvarying-stream [of] cognition - dhyānam.
Here, attention keeps resting on its object [mental representation] without shifting elsewhere and causes a steady single flow of cognition.
Consider the analogy of movie films. When snapshots taken at high speeds are replayed at speeds higher than 60 frames per second, our eyes or brain doesn't notice the discontinuities and movement appears continuous.
Similarly, our attention may rest on something, move away, and come back quickly without our noticing. This is normal thinking. But if it stays for just 12 continuous seconds, that is dhāraṇā. If that 12 seconds extends to 12x12 or 144 seconds or ~2.5 minutes, that causes the cognition flow called dhyāna. This light, free, effort-less - yet wilful - resting or training of attention for such short periods results in the flow of cognition called meditation.
dhāraṇā can be, and is done, very easily every day without conscious awareness. dhyāna, while not uncommon on a daily basis, is more likely to be sets of discontinuous dhāraṇā where the discontinuities or breaks between 12+ seconds of attention are not noticed.
Of Patañjali's aṣṭa-aṅgas (8 stages), in the stages or aṅgas listed before pratyāhāra, attention is outward - beyond the body, on others, on other things, different from me.
In pratyāhāra, there is a shift or turn from outward - bahiraṅga - to inward - antaraṅga.
And the rest are completely inward or mental processes.
The inwardness of dhāraṇā-dhyāna-samādhi should be understood very clearly because while they can indeed occur during outward activities or engagement, they are defined by the quality of mental attention during the activities, and not by physical or mental activities themselves.
samādhi
tad-eva artha-mātra nirbhāsam svarūpa-śūnyam iva samadhiḥ 3.3 PYS
That-itself meaning/essence/perception-alone shining [with] self-ness-void [of mind] itself - samādhi.
That [single-unvarying cognition stream] itself [results in] meaning-alone [of object of meditation] shining with null self-ness/activity [of mind] itself - samādhi.
Here, the meta activity of the mind ends, i.e., the mind stops thinking about what it is doing, that it is paying attention or in a cognition flow. Or at least it pauses for a long while!
That is, shifting between the activity itself - attention on an object of meditation plus cognising it - and thinking about the kind of mental activity (attention to what I am doing) halts. Then, only the object's meaning or essence floods the mind-field completely.
saṁyama
trayam-ekatra saṁyamaḥ 3.4 PYS
Triad/triplet-as-one - saṁyamaḥ [union/summation process]
Imagine the quality of your attention as it rests easily, lightly, happily upon something for a brief while, which then becomes a short while, and that in turn becomes a long while.
Specifically, for 12, 12x12, and 12x12x12 seconds. Or 12 seconds, ~2.5 minutes, ~half an hour.
It is easy to appreciate that the frenetic taking in of sensations slows down. It's like someone telling you,
"Ree-laaaa-xxx...
Take a deeeep, sloooow, breath...
Caaalm dooown...
And now...
look at that object."
Imagine then that same restful, peaceful, light, effort-less attention continues to stay on that same thing for a longer duration, and then for a really extended duration. Attention becomes cognition and then a silent mind-field imbued and flooded by meaning or essence.
Imagine the quality of your attention at the end of that extended duration!
Now imagine doing that with tenderness, affection, love for an extended duration - almost half an hour. What would your mind and brain and heart be like?
Finally, after practising for many, many, many half hours,
say a 1000 or even just a 100 of them,
imagine that you can build up to that same quality of attention in minutes or even seconds.
You have then compressed
12 seconds of attention = dhāraṇā -
extending to 144 seconds of attention = dhyāna -
extending to 1728 seconds of attention = samādhi,
I repeat,
compressed 1728 seconds of clock time worth of
binding-to-cognition-to-mind-field-flooding,
into a few minutes or even a few seconds of clock time of samādhi-quality attention.
Imagine samādhi - your entire mind-field flooded by the essence or meaning of an object - in seconds! Well, OK, in minutes :-)
This is saṁyama.
Meta modes - 'I' or subject, 'am doing' or 'verb'-ing - do not kick in now, implying greater efficiency in mental processing.