The term, cross-section fixed effect, refers to a constant term (i.e., non-varying component over time) that is potentially different for each firm in the sample. Thus, it is a 'fixed effect' over time but can vary for each firm. It represents unique effects that are specific to the firm that do not vary over time (e.g., the bank's specific geographic region of operation which might be very prosperous or very economically depressed).

The term, time fixed effect, refers to a constant term (i.e., non-varying component across firms at a point in time) that is potentially different for each time period in the sample. Thus, it is a 'fixed effect' for each firm on a cross-sectional basis but can vary from one time period to another. It represents unique effects that are specific to each time period but do not vary over firms (e.g., a negative industry-wide impact on capital ratios due to covid pandemic period).

I agree with Mr. @Michael S. Pagano....but If you expect a bit more detail please go this book...Angrist, J. D., & Pischke, J.-S. (2008). Mostly harmless econometrics: An empiricist's companion: Princeton university press.

Eugenio Paladino , my two cents:

Let's say you have a bivariate model of 3 firms (cross-section i) over 2 years (time dimesion, t):

(1) y_it = x_it + e_it

Note that there is no constant in (1).Let's add cross-section fixed effects to (1):

(2) y_it = x_it + f_1 + f_2 + f_3 + e_it

where f_1 is a binary variable equal to 1 for firm 1, f_2 is a binary variable equal to 1 for firm 2, and f_3 is a binary variable equal to 1 for firm 3. One of f_* is treated as the reference category in (2) and excluded to avoid perfect multicollinearity.

Now let's add time fixed effects to (2):

(3) y_it = x_it + f_1 + f_2 + f_3 + f_(t=1) + f_(t=2) + e_it

for f_(t=1) a binary variable equal to 1 for year 1, and f_(t=2) a binary variable equal to 1 for year 2. Again to avoid multicollinearity, only f_(t=1) or f_(t=2) are included in the estimation to avoid perfect multicollinearity. E.g., the model below is a longitudinal model of the effect of x on y for firms 1,2,3 over the years 1,2, including cross-sectional fixed effects, time-series fixed effects and a constant(c):

y_it = c + x_it + f_1 + f_2 + f_(t=2) + e_it