As an empirical fact, the very same person is much more likely to win an election if that person in an incumbent than if that person is not and there is an open race, or a candidate is challenging an incumbent.
This is because, among other things, an incumbent has better name recognition, challenges to an incumbent from a member of the same political party are strongly disfavored (even though that party is likely to be the one preferred by most voters in that politician's district), an incumbent doesn't need to spend time engaged in non-political work for economic self-support, and an incumbent can't manipulate the levers of government to make the incumbent appear desirable in superficial ways that don't reflect the bigger issues that really matter in governing a political unit.
Term limits periodically wipe out incumbency advantages so that the vote of the people reflects an unbiased view of their wishes prospectively rather than being influenced by the mere fact that someone has previously held the same post.
This keeps elected officials in line with the wishes of the people, and also prevents incumbency advantages (like gerrymandered districts that put strong opponents in the same district while leaving incumbents in districts that lack strong challengers) from further accumulating over time, which may create an environment akin to a dominant party system, where there is a legal opposition but it has no realistic prospects of winning important political prizes in the near term.
If an elected official is very hard to remove despite the formal electoral process due to incumbency advantages, at some point the elected official can effectively ignore the public and rule as he or she sees fit at whim, must like a dictator. This isn't an absolute freedom and an extreme act could get an opposition figure elected (if those in charge don't change the election laws to prevent that), but even a dictator still needs to maintain a basis of support and legitimacy to rule.
There are many examples in newer democracies of Presidents or other leaders improperly manipulating, greatly postponing or even entirely dispensing with elections creating a one party state or a publicly acknowledge dictatorship. The threat is not hypothetical.
Regular shifts in who holds political office through an electoral process (which may include term limits) is necessary, as an empirical matter, for a democratic electoral system to be healthy and functional.
As one empirical example, jurisdictions with term limits tend to have more women, and generally more diverse groups of elected officials and the lagging indicator influences of incumbency are overcome.