STRs are marker values, like DYS391=10. See here for an explanation of how this value is measured and what it means. An STR signature is a pattern of STR markers that is uncommon enough to characterise a genetic cluster.

SNPs are the addition, deletion or mutation of a genetic base. For example, the SNP M269 defines a large subclade of haplogroup R1b.

To understand the genealogical significance of these genetic features, consider the task of locating a building.

Postal codes define a broad geographical area, like SNPs define a collection of related people (a subclade). Just as a reference book is needed to determine which area a postal code refers to, an index of SNPs is needed to make sense of the SNP name. Recent SNPs are more precise than older SNPs in the same lineage. For example, R1a-Z283 is a subset of R1a-M417. Just like ZIP+4 code 90210-1234 is a region within ZIP code 90210.

STR signatures are more descriptive, but they can be ambiguous. Similar to how "the house at the bottom of the hill with a pond and a weeping willow tree" can describe many houses in many cities, a 12-marker STR pattern can be found in many individuals that are not related within a genealogically relevant timeframe.

So STR and SNP results are complementary, and most powerful when used in tandem. Just like using building descriptions and postal codes together give you a better chance of locating the correct building.

Be warned that there is no genetic genealogy analogue to a mailing address. STRs and SNPs in tandem can still be ambigious: a man could theoretically have the same 67-marker STR signature and terminal SNP as his fifth cousin with the same surname. Just like "the official gated residence situated in post code block SW1A of London" could refer to either Buckingham Palace or 10 Downing Street.