Weight is the thickness of the letters. Although regular fonts you see in Microsoft Office may only have a few weights, specialty typefaces can easily have a dozen weights. Generally, heavier-weighted fonts (ie. Bolder ones) are reserved for emphasis text
Slope is how slanted a letter looks. You may know it as italic or oblique type. Oblique refers to a font that has been skewed in one direction. Many sans-serif fonts will have oblique typefaces. Meanwhile, Italic refers to a font whose letters have actually been drawn differently in the slanted version.
Also known as Stretch, a font’s width is literally how stretched out it is horizontally. Conversely, narrower fonts are often called compressed, or condensed. Usually, sans-serif fonts are commonly issued at various widths, whilst serif fonts only come in regular width.
Serif is a small little drop added to the corners/edges of letters. Typefaces are either serif (Times New Roman, Cambria, Georgia for example) or sans-serif (Arial, Helvetica, Century Gothic). Many studies show that sans-serif fonts are harder to read, despite their recent popularity.
Font metrics are the measurements surrounding a letter. Usually, measurements are relative to the baseline, the invisible line upon which a line of text sits. The distance from the baseline to the top of the letter is the ascent. The distance from the baseline to the bottom of the letter is the descent. Furthermore, the distance from the ascent to the descent is the leading. Meanwhile, the height is considered the sum of all three.
Some other terminology includes cap height – the height of capitals, x-height – the height of lowercase letters. Kerning is a practice whereby fonts are fitted closer together.