What are the groups that NaBH4 can and cannot reduce?

(1) NaBH4 is a milder and selective reducing agent than LiAIH4. It can reduce aldehydes,  ketones and acid chlorides without attacking other reducible groups such as esters epoxides, catboxylic acids, esters, amides olefIns etc.

(2) NaBH4 is also used in the second step of the Oxymercuration Demurcuration addition reaction to replace mercury (Hg)(Demurcuration) with H

NaBH4  can reduces:  

(1) Aldehydes into primary alcohols.     

(2) Ketones into secondary alcohols.  

(3) Acid chlorides into primaryalcohols.

 NaBH4 can't reduce:

Acids, Amides, Esters, anhydrides, Nitriles, Isonitriles, alkenes, alkynes etc.

Why NaBH4 is milder reducing agent than LiAlH4?.

LiAlH4 and NaBH4 both are reducing agent and use for reduction of polar multiple bond (>C=O ,-CN ). But LiAlH4 is stronger than NaBH4 because NaBH4 breaks into Na+ cation and BH4 -  anion.  Now, BH4 - ion breaks into BH3 stable ground state and protonates H - ion ie. Hydride ion and this hydride ion acts as a reducing agent.  In BH4 - ion Boron is more electronegative atom as compared to aluminum in AIH4 - ion. Thus, reducing power of hydride ion gets lowered as boron withdraws more electrons towards itself as compared to Aluminlum, so the hydrides of aluminum are more reducing in nature than hydrides of baron.

What are the groups that LiAlH4 can and cannot reduce?

Lithium aluminium hydride (LiAIH4) is a nucleophilic reducing agent, and used to reduce polar multiple bonds like >C=O, -CN bond because it is hydride (H-) donor. And it is simply abbreviated as LAH.

LIAIH₄ can reduce:
(1) Aldehydes to primary alcohols,
(2) Ketones to secondary alcohols,
(3) Carboxylic acids and esters to primary alcohols.
(4) Acid chlorides to primary alcohols.
(5) Ester to primary alcohols.
(6) Acid anhydrides to primary alcohols.
(7) Amides and nitriles to primary amines.
(8) Isonitriles to secondary amines.
(9) Epoxides (Cyclic ethers) to alcohols.
(10) lactones (Cyclic esters) to diols. 

Important Notes:
LiAH4 can reduce Aldehydes, ketones, carboxylic acids, ester, acid chlorides, acids anhydrides, acid amides,  Nitro Compounds and nitriles and isonitriles  without attacking (Isolated non polar bonds , like -C=C- ) double bonds present in the Compounds. The only exception in this case alpha- Beta unsaturated compounds containing phenyl group in the Beta position, in this case LiAH₄ also attack on double bond.
We can say that the double or triple bonds in conjugation with the polar multiple bonds can be reduced.