The Grignard reagent features a more or less direct bond between a carbon centre and a metal centre: #RH_2C^(delta-)""^(+delta)MgX#, or even as a full-blown carbanion, #RH_2C^(-)""^(+)MgX#. Given this formulation, its interaction with a carbonyl species may be rationalized.
The Grignard will react with an aldehyde to form (after workup) a #2^@# alcohol, with a ketone to give a #3^@# alcohol, with carbon dioxide, and ethylene oxide, to give a carboxylic acid, or a primary alcohol respectively. All of these are examples of prized #C-C# bond forming reactions.
Of course, the ipso carbon on each substrate is somewhat electron-poor, i.e. electrophilic, viz., #""^(delta-)O=C^(+delta)=O^(delta-)#. Upon addition of the Grignard, (which you can usually do by pouring the ethereal solution of #RMgX# directly onto dry ice) a direct #C-C# bond is formed between the Grignard residue and the carbonyl. This gives a carboxylate salt, and after workup, a carboxylic acid that is 1 carbon longer than the original Grignard residue.
With a ketone, acetone, a #3^@# alcohol is formed:
#R_3C^(delta-)""^(+delta)MgX +R'_2C(=O) rarr R'_2(""^(-)O)C-CR_3#
If it were acetone, then the alcohol product would be #(H_3C)_2C(OH)R#.
All of this demands fast-working, being on the ball, and reasonably dry solvents. Today, you can even buy pre-prepared solutions of Grignard and lithium reagents for direct use in synthesis.
Can you predict the product between acetone and methyl magnesium chloride?