There is no country "sandwiched" between Estonia and Lithuania in the sense of a tiny enclave; rather, Latvia occupies the entire land border between its two Baltic neighbors.
The Baltic states—Estonia (north), Latvia (middle), Lithuania (south)—form a contiguous chain along the eastern shore of the Baltic Sea.
All three were independent republics (1918–1940), annexed by the USSR (1940–1991, interrupted by Nazi occupation), and restored independence in 1990–91. All joined NATO and the EU in 2004 and the Eurozone (Estonia 2011, Latvia 2014, Lithuania 2015).
Yet they are linguistically and culturally distinct: Estonian is Finnic (related to Finnish); Latvian and Lithuanian are the only surviving Baltic languages (Indo-European), mutually unintelligible. Lithuania has a historic Polish minority and Catholic dominance; Latvia has a large Russian-speaking minority and Lutheran/Catholic mix; Estonia is largely secular and Lutheran.
Driving from Tallinn (Estonia) to Vilnius (Lithuania) takes ~4.5 hours via Riga (Latvia) on the Via Baltica highway. There are no internal border controls (Schengen). Latvia is not merely "between" them—it is the central link, the largest by territory (64,589 km²), and the historic crossroads of the region.