This question is a fairly open-ended one, and it is also subjective: it asks for your own impressions, so it isn't possible to give one single answer. However, a good place to start might be by reading the poem and identifying what elements of Anglo-Saxon life seem to stand out most strongly.
For example, you might consider the sort of language the speaker in the poem uses when he describes his life. It doesn't sound as if it's been an especially easy existence for him. On the contrary, the Seafarer promises to tell a "true song" about himself and goes on to elucidate that this means "days of struggle" which have been filled with "sorrow" and "worries." There is also a semantic field of entrapment, conveyed through words like "fettered," "bound" and "clasps." This certainly creates an impression that Anglo-Saxon life could be extremely punishing, that the weather was cold and unfriendly, and that sometimes times were very hard.
As we proceed through the poem, the Seafarer's situation remains dire, but we can also get a better sense of why. The speaker tells us that he is missing "friendly kinsmen" and that part of the reason he feels so "wretched and sorrowful" is that he is forced to walk "the paths of exile." We can assume, therefore, that the speaker is used to being part of a close-knit group of people. This gives the impression that Anglo-Saxon society set great stock by being part of a family or clan grouping, and that this was one of the chief sources of happiness for most Anglo-Saxons.
The speaker in the poem also discusses at length what a Lord would do for his vassal. He describes how his Lord would give him rings, which symbolized the connection between Lord and servant. The speaker goes on to say that he also misses "pleasure in woman." From this, we might derive the impression that Anglo-Saxon society greatly valued and privileged the relationships between men, and that these provided comfort just as much as relationships between men and women.
The poem also gives us some idea of how Anglo-Saxons viewed their legacy. The speaker is obviously a Christian, eager to experience "joy with the Hosts," but he also details the importance of having "valorous deeds" passed down to others. This gives the impression that the Anglo-Saxons greatly valued heroism, and being remembered as a hero in the eyes of others.