Direct answer
Cohort analysis groups users by something they share at a fixed point in time, most commonly the week or month they signed up, and then tracks how that group behaves over subsequent periods, so that you are comparing like with like instead of blending users at very different points in their lifecycle into one trend line. An acquisition-date cohort is the most common type (grouped by signup date), and a behavioral cohort groups by a shared action instead, such as everyone who first used a specific feature in the same week.
Structured elaboration
The reason cohort analysis exists as a distinct technique, rather than just looking at a daily or weekly trend of an overall metric, is that an aggregate trend conflates two very different things: how existing users are behaving, and how the MIX of users is changing as new people join. If a product is growing fast, an aggregate "percent of users active today" trend can look flat or even improve while every individual cohort is actually retaining worse, purely because a large influx of very recent (and therefore still highly active) signups is diluting the picture. Reporting metrics by cohort instead removes that mixing effect and lets you ask a cleaner question: for people who joined at the same time, how does their behavior change as they age?
At least three retention metrics are typically reported for a cohort: day-1 retention (the fraction still active exactly one day after joining), day-7 retention (the same at one week), and rolling retention (the fraction active at any point on or after a given day, rather than on exactly that day), each answering a slightly different question about how quickly and how durably a cohort settles into use.
A concrete business use case: an e-commerce company noticing that customers acquired through a paid-search channel show markedly worse 30-day retention than customers acquired organically, even though both channels show similar day-1 numbers, would use that cohort comparison (not a blended trend line, which would hide the channel difference) to justify shifting acquisition budget toward organic-adjacent channels or investing in a channel-specific onboarding experience for paid-search users.
Worked example
A cohort of 200 users who all signed up in the same week produced the following illustrative weekly active counts: week 0 (signup week) 200 active, week 1: 110 active, week 2: 84, week 3: 68, week 4: 58, week 5: 48, week 6: 40, week 7: 34. The retention percentage for each period is the active count divided by the original 200, giving 100%, 55%, 42%, 34%, 29%, 24%, 20%, and 17%. If a second cohort acquired one month later, in a period when a new onboarding flow shipped, showed week-1 retention of 68% instead of 55% on a comparably sized cohort, that comparison (holding cohort size and week-offset fixed) is a much stronger signal that the onboarding change helped than comparing two different weeks' overall daily-active-user numbers, which would also move for reasons unrelated to the change, such as normal week-to-week traffic variation.
Trade-offs and pitfalls
Common pitfalls include comparing cohorts of very different sizes without normalizing to percentages (a cohort of 20 users retaining "50%" is much noisier evidence than a cohort of 20,000 doing the same), treating cohort analysis as interchangeable with a simple daily trend line when the two answer different questions, and forgetting that a cohort acquired very recently has an incomplete observation window, so its later-period numbers should not yet be compared directly against an older cohort's fully-observed numbers.