The speaker actually says active service here, rather than acts of service. However, acts of service refers to actions (in intimate relationships and as related to the love languages) that are meant to be thoughtful and helpful for your loved ones, such as cooking them a meal when they're tired, helping them with their work when they're busy, and so on.
Ex: My primary love language is acts of service.
Ex: My boyfriend isn't good with words, so he prefers to show his love through acts of service.