What is beat-synchronous chroma?
Short answer

Normally a chromagram constits of chroma feature vectors per time frame. If you want to have a musical time axis in beats instead of a physical time axis in seconds, you have to get beat information (e.g. by a beat tracker) and average all chroma features that belong to the time span of a beat.

Long answer

Since the comments asked for a longer answer, here it is: A chromagram presents the energy that is contained in the twelve pitch classes over time. Starting from the STFT, you could compute a chromagram version by summing up all frequency bins that correspond to a particular pitch class, individually for each time frame. Since the STFT uses a constant hopsize, you end up with a chromagram which is constant in physical time. Since chromagrams are used for music applications, it is sometimes desirable to have a musical time axis, e.g. in beats. Since the tempo of music can change, the physical time span of an beat can vary. For converting physical to musical time, you could annotate the beat positions within the music or apply an automated procedure, kown as beat tracking. Then you could simply average the chroma features that belong to the time span of a beat.

In more technical wordings: $\mathcal{C} \in \mathbb{R}^{N \times 12}$ is your normal chromagram matrix with $N \in \mathbb{N}$ time frames. $\mathcal{B} : \mathbb{N} \rightarrow \{s| s \subset \{1,\dots,N\}\}$ is a function that gets the index of a beat as input and outputs a set of all time frame indices belonging to this beat index. You want to compute the beat-synchronous chromagram $\mathcal{C}^\text{beat} \in \mathbb{R}^{B \times 12}$ for $B \in \mathbb{N}$ beats. Usually $N \gg B$. You can do this simply like this: $\mathcal{C}^\text{beat}_{b, c} = \frac{1}{|\mathcal{B}(b)|} \sum_{n \in \mathcal{B}(b)}  \mathcal{C}_{n, c}$ with beat index $b \in \{1,\dots,B\}$ and pitch class index $c \in  \{1,\dots,12\}$.

This is not the place for comprehensive literature, but only two references for general chromagrams and beat-synchronous ones:

Meinard Müller: Fundamentals of Music Processing, Springer 2015. (Chapter 3.1)

Daniel P. W. Ellis and Graham E. Poliner: Identifying Cover Songs with Chroma Features and Dynamic Programming Beat Tracking, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Honolulu, 2007, pp. IV-1429–IV-1432.