A separation in which the mobile phase composition remains constant throughout the procedure is termed isocratic (meaning constant composition). The word was coined by Csaba Horvath who was one of the pioneers of HPLC.
The mobile phase composition does not have to remain constant. A separation in which the mobile phase composition is changed during the separation process is described as a gradient elution. For example, a gradient can start at 10% methanol in water, and end at 90% methanol in water after 20 minutes. The two components of the mobile phase are typically termed "A" and "B"; A is the "weak" solvent which allows the solute to elute only slowly, while B is the "strong" solvent which rapidly elutes the solutes from the column. In reversed-phase chromatography, solvent A is often water or an aqueous buffer, while B is an organic solvent miscible with water, such as acetonitrile, methanol, THF, or isopropanol.
In isocratic elution, peak width increases with retention time linearly according to the equation for N, the number of theoretical plates. This can be a major disadvantage when analyzing a sample that contains analytes with a wide range of retention factors. Using a weaker mobile phase, the runtime is lengthened and results in slowly eluting peaks to be broad, leading to reduced sensitivity. A stronger mobile phase would improve issues of runtime and broadening of later peaks but results in diminished peak separation, especially for quickly eluting analytes which may have insufficient time to fully resolve. This issue is addressed through the changing mobile phase composition of gradient elution. 
By starting from a weaker mobile phase and strengthening it during the runtime, gradient elution decreases the retention of the later-eluting components so that they elute faster, giving narrower (and taller) peaks for most components, while also allowing for the adequate separation of earlier-eluting components. This also improves the peak shape for tailed peaks, as the increasing concentration of the organic eluent pushes the tailing part of a peak forward. This also increases the peak height (the peak looks "sharper"), which is important in trace analysis. The gradient program may include sudden "step" increases in the percentage of the organic component, or different slopes at different times – all according to the desire for optimum separation in minimum time.
In isocratic elution, the retention order does not change if the column dimensions (length and inner diameter) change – that is, the peaks elute in the same order. In gradient elution, however, the elution order may change as the dimensions or flow rate change. if they are no scaled down or up according to the change
The driving force in reversed phase chromatography originates in the high order of the water structure. The role of the organic component of the mobile phase is to reduce this high order and thus reduce the retarding strength of the aqueous component.