Tickrate is the number of times per second that the server recalculates what's happening in a match: player positions, bullet hits, grenade explosions, round economy. The higher the tickrate, the more often the server "checks in" with reality, and the more precisely it registers events. The value is usually given as a number — for example, 64 or 128 — representing the number of ticks (updates) per second.
Why it matters
In practice, tickrate directly affects hit registration. Between two ticks, the server doesn't see what's happening — it's essentially taking a snapshot of the game at regular intervals. At a low tickrate, these intervals are larger, and there's a chance that fast movement or a shot fired within a narrow window of time will be processed with a delay or less accurately than the player expected. At a high tickrate, there are fewer such "blind spots," and hits are registered closer to what the player actually saw on their screen.
This is exactly why tickrate is a constant topic of debate among those who follow the competitive scene: official tournaments and professional servers usually run a higher tickrate than the public servers available to any player. The difference shows up in small things — how predictably spray control (managing weapon recoil during automatic fire) behaves, how fairly clutches (situations where a single player wins a round alone against multiple opponents) are decided at the very edge of the round timer.
Where the term comes from
The term comes from server architecture in games in general, not something invented specifically for Counter-Strike — a "tick" as a unit of game time is used across various projects with server-side logic. In the CS community, the word stuck because players notice the difference between servers in practice: some feel "more responsive," while others feel like there's a slight delay between an action and its result. That's where the casual phrases "a server on 64 ticks" or "playing on 128 ticks" come from — this is how players describe the quality of registration, even before getting into the technical details.