The tablespoon is a unit of volume in the US customary system and uses the symbol Tbsp.
In the kitchen, the tablespoon is the larger of the commonly used spoons served at the table and represents 1/2 US fluid ounce or, expressed in SI / metric format; 14.78676 ml.
This is often expressed as equivalent to 3 teaspoons (3 Tsp) although strictly speaking it is a little under the size of 3 metric teaspoons (5 ml) at 4.92892159375 ml. It was established to assist normal kitchens with recipes without the need for specific measuring equipment or devices. Although many spoons differ in sizes (and very rarely is a spoon filled accurately) it allowed for a decent "catch-all" and gave a "good enough" result most of the time.
The barrel is a unit of volume used in the oil industry with the symbol bbl.
Oil is more commonly expressed in terms of cubic metres (m³) but in the US and in the economic world (mainly because such a large percentage of the world's oil is shipped to the US) as barrels.
The measurement of the barrel originated in the US at the first oil well in Pennsylvania. There were so many variants of barrel size (including those used for wine and other goods) that the distrust became so prevalent a central and standard barrel size was created. This was finally established in 1872 as 42 US gallons.