This is the classic card game Cassino (also known as Casino or California Cassino), an interesting "fishing" game.

A regular 52 card deck is used. Each numeral card (ace-ten) is counted as its numerical value (ace = 1, two = 2, etc). The aim is to capture cards from a layout on the table, by playing a card from your hand which matches in number a table card or the sum of several table cards.