Resolution is a measure of the smallest unit or sample in data that can be distinguished from any other, and/or the number of samples for a given unit.
In GIS this often refers to spatial or ground resolution of raster cells or pixels. For example SRTM data can be available at resolutions of 90m or 30m, where one cell with a single, constant elevation value is assigned to a square on the ground 90m or 30m on a side. Satellite imagery is often discussed in terms of resolution, where one image pixel represents 0.5m (high), 15m (mid), or 30m (low) square on the ground. Descriptors such as 'high' and 'low' are somewhat arbitrary, but demonstrate resolution values have a range or spectrum similar to map scales ('large' and 'small').
However resolution also applies to the values measured for that unit of ground distance. In the case of SRTM there is also a vertical resolution since that data measures elevation. Contour lines can easily demonstrate this - each line in the data may represent a difference of 1m, 5m, or 100m. Examples of other types of resolution include spectral (width on the EM spectrum covered by a single band), temporal (time between samples - minutes, days, or years), or radiometric (the strength or magnitude of a signal).
Note that resolution applies to vector data as well as raster or value. The same section of sinuous river could be represented with a dozen points or a hundred. The more samples along the line, the more detail or resolution with which that feature can be represented in the data.
Resolution is also often discussed in terms of output, be it screen image or paper. Pixels per inch (ppi) and dots per inch (dpi) are frequently used interchangeably, though the former is for electronic display (and varies by display rather than source image) and the latter for print. This is effectively a second scale on top of the map scale - ground unit to pixel and then pixel to output unit.