1080i is one of the HDTV formats. It means the image has 1080 lines of "vertical resolution", i.e. 1080 pixels from top to bottom. The i stands for interlaced (see below).
1080i video usually has 1920 lines of horizontal resolution, making a total image size of 1920x1080 pixels and an aspect ratio of 16x9.
There are some variations; for example, HDV has a resolution of 1440x1080 but maintains a widescreen aspect ratio by using rectangular pixels.
1080i is similar to 1080p, except that it uses the interlaced format rather than progressive. This means that each frame consists of two fields each showing only half the pixels. One field shows the odd lines, the other field shows the even lines.
1080i can be specified as 1080i25 or 1080i30 — the additional number refers to the number of frames per second (fps). Traditionally, PAL countries use 25fps, NTSC countries use 30fps.