Liability is built on binding. The word traces through Anglo-French liable (bound, obligated) from Old French lier (to bind), from Latin ligare (to tie). A liability is, at root, something you are tied to — an obligation that binds you until it is satisfied. The English suffix -ability converts the adjective liable into a noun naming the condition of being bound.
In accounting, liabilities are financial obligations a business owes to others: loans, accounts payable, wages owed, taxes due. They appear on the right side of the balance sheet, opposite assets. The accounting equation — assets equals liabilities plus equity — frames the entire discipline around what a company owns versus what it owes. Liability in this context is the discipline's most fundamental term.
Legal liability has a broader scope. Being liable means being legally responsible for something, whether a debt, a contract, a tort, or a regulatory obligation. Limited liability, the principle that company shareholders cannot lose more than their investment, was one of the most consequential legal innovations of the 19th century. It encouraged investment by capping the financial binding — you were tied to your stake but no further.
The informal sense — he's a liability to the team — extends the metaphor from financial and legal binding to general disadvantage. A liability in this sense is a drag, a weight that ties you down and limits your effectiveness.
Latin ligare produced one of the richest word families in English. Alliance (binding together), ligament (tissue that binds bones), oblige (to bind by duty), rely (to bind back to), liaison (a binding connection), lien (a legal claim binding property), and liana (a binding vine) all descend from the same root. The concept of tying and binding runs through English vocabulary for duty, anatomy, diplomacy, botany, and law.