Interlacing refers to the method of encoding two separate "fields" in a single frame by using alternating lines, storing the first field in odd-numbered lines and the second in even-numbered lines or vice versa. When displayed on a traditional (CRT) television, the second field is displayed as the first one is fading out, fooling the eye into seeing them as separate frames; this gives the illusion of a doubled frame rate (59.94 (NTSC) or 50 (PAL) fps instead of 29.97 or 25). However, when such video is viewed on a computer, it gives the so-called "window-blind" or "comb" effect (visible as little horizontal bars where the two fields do not match), because both fields are displayed at the same time. Video files used on PCs are often stored in progressive (non-interlaced) format to avoid this problem, but are not quite as smooth as interlaced video viewed on a television.
Note that if you have an interlaced source file that you want to transcode for watching on a PC, you should not deinterlace (convert interlaced video to progressive format) during transcoding! Most video players have options to deinterlace during playback; by leaving the video in interlaced format, you can take advantage of improvements in deinterlacing algorithms without having to re-encode the video. If you deinterlace the video when you transcode it, then you have no way to recover the original interlaced data, and you'll have to re-encode from the source if someone comes up with a better deinterlacing method.
Comparison of deinterlacing methods: http://guru.multimedia.cx/deinterlacing-filters/
Note that the comparisons shown on that page are somewhat artificial... You will need to experiment with the yadif and mcdeint options on a movie yourself to decide whether they should really be used in combination. My experiments showed very surprising results!!
Interlacing and camcorders
Most DV cameras record in interlaced mode, either exclusively or by default. If you intend your video to be watched only on PCs, you have the option of deinterlacing the video--in other words, merging each pair of fields into a single progressive frame--but since this modification can't be undone, it is usually more desirable to encode the interlaced fields as-is. The problem, however, comes in determining which field should be displayed first: the top field (lines 1,3,5,...) or the bottom field (lines 2,4,6,...). In NTSC regions, most cameras seem to use bottom-field-first; the --encode_fields b option, shown above, indicates this to transcode. PAL, on the other hand, uses top-field-first, which is indicated with --encode-fields t. (However, DV video always uses bottom-field-first format, even in PAL areas; you may need the "fields" filter: -J fields=flip to get correct display.) If you get the option wrong, there will be no difference on a PC monitor, but when viewed on a TV the video will be very jittery; in this case, try the opposite setting.
Some cameras also have the option to record in progressive mode. If you are intending the video to be seen primarily on a PC monitor, or if there won't be any rapid movement (such as at a house party), progressive recording is probably your best choice, since it ensures the video can be watched both on PCs and TVs as is. In this case, use --encode_fields p to tell transcode that the video is progressive.