My favourite theorems in mathematics are the ones that at the same time great and have easy-to-understand formulation. To put aside various P=NP claims in arxiv, I will concentrate on theorems that where peer-reviewed and published in 2021. Most of them appeared in arxiv before.
So, the greatest easy-to-understand theorems published in 2021 are:
Theorem of Annika Heckel about non-concentration of the chromatic number of a random graph https://www.ams.org/journals/jams/2021-34-01/S0894-0347-2020-00957-2/
A dramatic progress on sunflower conjecture by Alweiss, Lovett, Wu and Zhang https://annals.math.princeton.edu/2021/194-3/p05
The resolution of the rectangular peg problem for smooth Jordan curves by Greene and Lobb https://annals.math.princeton.edu/2021/194-2/p04
Characterization of fields of values of odd-degree irreducible characters by Navarro and Tiep https://www.cambridge.org/core/journals/forum-of-mathematics-pi/article/fields-of-values-of-characters-of-degree-not-divisible-by-p/0FE327DAE6088EC9B43A0CFAFC8E8D52
Proof that the Dehn function of $\mathrm{SL}_4({\mathbb Z})$ is quadratic by Leuzinger and Young https://annals.math.princeton.edu/2021/193-3/p02
Proof that the group $\mathrm{Aut}(F_n)$ has Kazhdan's property (T) for all $n \geq 6$ by Kaluba, Kielak and Nowak https://annals.math.princeton.edu/2021/193-2/p03
Characterization of $\frac{3}{2}$-generated groups by Burness, Guralnick and Harper https://annals.math.princeton.edu/2021/193-2/p05
A counterexample to the unit conjecture for group rings by Gardam https://annals.math.princeton.edu/2021/194-3/p09
Proof of the universal optimality of the ${E}_8$ and Leech lattices by Cohn, Kumar, Miller, Radchenko and Viazovska https://annals.math.princeton.edu/articles/17703
New bounds on the density of lattice coverings by Ordentlich, Regev and Weiss https://www.ams.org/journals/jams/2022-35-01/S0894-0347-2021-00984-0/home.html
Determining, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separated by the given angle by Jiang, Tidor, Yao, Zhang and Zhao https://annals.math.princeton.edu/2021/194-3/p03
The isoperimetric inequality for minimal surfaces by Brendle https://www.ams.org/journals/jams/2021-34-02/S0894-0347-2021-00969-4/
A connection between thresholds and fractional expectation-thresholds established by Frankston, Kahn, Narayanan and Park https://annals.math.princeton.edu/2021/194-2/p02
An almost constant lower bound of the isoperimetric coefficient in the KLS conjecture by Chen https://link.springer.com/article/10.1007/s00039-021-00558-4
An $O(n \log n)$ algorithm for multiplication of $n$-digit integers by Harvey and van der Hoeven https://annals.math.princeton.edu/2021/193-2/p04
An explicit construction of polynomials with optimal condition number by Beltran, Etayo, Marzo and Ortega-Cerd https://www.ams.org/journals/jams/2021-34-01/S0894-0347-2020-00956-0/
I am sorry if you think that this list is too long but in my opinion all these theorems are both great and beautiful, so I will let you to choose your own 3-5 favourite ones.
Finally, you may want to look at my book https://link.springer.com/book/10.1007/978-3-030-80627-9 with the descriptions of all such theorems published from 2001 until now.