An acetal is a carbon between two oxygens of the form R-O-CHR-O-R, so a hemiacetal can be considered half an acetal - since it is R-O-CR-O-H which has an R group replaced by OH.
Attacking a ketone gives a hemiketal:
Since the hemiketal is of the form R-O-CR2-O-H, you can use the above argument to work out what a ketal is.
Most hemiacetals and hemiketal are unstable, since R-O- is a good leaving group (ie. easily expelled).
C=O has a strength of 720kJ/mol, while C-O is 350kJ/mol, so the energy is favorable.
A cyclic hemiacetal is called a lactol, and is usually more stable, but still in equilibrium with its open form. Five and six-membered rings are particularly stable due to their low strain. The most important examples are many sugars:
These two examples can form 5 and 6 membered rings (pyranoses and furanoses) depending on which alcohol attacked the C=O. Six-membered rings predominate for both sugars as you would expect. The alpha and beta stereoisomers depend on whether the OH attacked from above or below the C=O.
The overall equilibrium lies far to the right - about 99% of these sugars in an aqueous solution are in cyclic form.
Similar to hydrates, non-cyclic hemiacetals can be stabilized by electron withdrawing groups. Hemiketals are less stable, but this logic presumably applies to them too.
The formation and decomposition of these compounds are catalysted by acids or bases:
In the presence of an acid, but not a base, an acid has an effect beyond being a catalyst. The acid will protonate the alcohol group, eliminate water and push the product all the way to an acetal:
Not everyone teaches the oxonium ion step, but chemists are confident that it exists. It would be incorrect to draw direct displacement:
It is possible to drive this reaction by removing water. Or, if the aldehyde is sufficiently reactive, simply having an excess of reagents:
Acetals can also be made by hydrolysis of ortho-esters:
Acetals in general can be hydrolysed easily by an acid, but are stable to a base. Cyclic acetals are more stable to hydrolysis, as you might predict.
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