Hardware refers to the machine heads (also known as tuning pegs), the bridge, and the controls. All of these can be replaced quite easily, so if you can only afford a cheap bass to start with, all is not lost - it can almost always be significantly improved at a later date, with little or no experience required.
The bridge of a bass is a critical part of the instrument, playing a big part in determining the way it sustains and responds. There are several ways that bass strings can be threaded through the bridge - some are top-loading, and others are strung through the body. 'Through-body' bridges improve clarity and sustain, but it can take a little longer to change strings. The other important function of the bridge is string adjustment - a good quality bridge will enable you to control the string height and tuning for each string. This, combined with fine adjustment of the truss rod (which controls the angle of the neck) will help you to keep your bass in perfect working order.
The machine heads tune the strings of your guitar. Cheap heads may slip while playing, causing the intonation of your instrument to drop. D-Tuners provide an easy way to detune your E-string down a tone to D via a simple pulley. But why stop at the E-string?!