In the paper, they state that the ‘social reward learning period’ is a critical period that they described in their previous paper:

Recently, we have discovered a novel critical period for social reward learning and shown that the empathogenic psychedelic MDMA is able to reopen this critical period[11].

Their previous paper that they cite is the following:

Nardou, Romain, et al. “Oxytocin-dependent reopening of a social reward learning critical period with MDMA.” Nature 569.7754 (2019): 116-120. (Scihub)

Here they are more specific about what they mean with a ‘critical period’:

A critical period is a developmental epoch during which the nervous system is expressly sensitive to specific environmental stimuli that are required for proper circuit organization and learning. Mechanistic characterization of critical periods has revealed an important role for exuberant brain plasticity during early development, and for constraints that are imposed on these mechanisms as the brain matures

And they point out that the term ‘social reward learning’ is described in the following paper:

Dölen, Gül, et al. “Social reward requires coordinated activity of nucleus accumbens oxytocin and serotonin.” Nature 501.7466 (2013): 179-184. (Scihub)

From this paper, the difinition is:

Growing evidence suggests that social interaction itself can act as a natural reward

So, putting it all together:

A social interaction can in itself produce feeling of reward. The ability to experience social interaction as a reward is not ‘innate’, but rather an acquired ability that requires the brain to undergo certain plastic transformations. There is a period during the early development of an animal in which the region of the brain that controls the social reward pathway is highly plastic and responsive to stimuli. This period is considered a critical period, because it is during this stage that the plastic brain can develop a topology that allows the animal to feel more or less strongly rewarded by social interactions. After the critical period of development has passed, this brain region is no longer very plastic, and so the ability of the animal to experience social interactions as a reward cannot easily be changed over time.

In this study, they show that it is possible to move the brain back towards the plastic state that is present during the critical development period, potentially allowing the mature animal to develop or increase its capacity to experience social interactions as a reward.