S.M.A.R.T. means
[SMART] means "Self-Monitoring, Analysis, and Reporting Technology". First developed in the 1992 by leading hard drive manufacturer, S.M.A.R.T. becomes a quasi standard to monitoring and tracking sensitive values from your drive to prevent hard drives from fail. The plan was, if a hard drive says 'I will die soon', the motherboard tell us, so we can backup and change quick the drive. Unfortunately this doesn't works very often.

Attributes, Values, Thresholds and S.M.A.R.T. examples
Attributes describes the measured value of hard drive controller operations.
The values of an attribute are: current, worst, threshold and raw. Values are normalized to a vendor specific scale. Scales could be ranged up to 100, 200 or 253. Often higher values are better than lower values. The threshold marks the value at which the hard drive could fail. The worst value is the baddest value seen for this drive at this attribute.
The raw value is a vendor coded count that give, after decoding, the normal values like current, worst and threshold.

S.M.A.R.T. Interpretation
First some important knowledge about threshold values. If threshold is 0 the attribute has only information character. If threshold is 253 the attribute is only for testing reason.
A typical attribute set could be:

• Attribute name: "Read Error Rate"
• Current: 253
• Worst: 253
• Threshold: 63
• Raw: 0

All right , this is a nice set. Nothing happens at this attribute. Only if this attribute reach the threshold value 63, we should have to change the hard drive.
Let's look on a attribute with a warning status:

• Attribute name: "Read Error Rate"
• Current: 113
• Worst: 85
• Threshold: 63
• Raw: 1234567

The hard drive have sector read errors in the past, but work fine for now and (perhaps) work fine in the near feature. However, I would now start to make more often backups and begin to plan a hard drive change.
It is difficult to make correct interpretations in general, because different vendors normalize values in different way. We can recommend to ask in vendors forum for interpretations if you are unsure.

Attribute Hit List
We will give a list of important attributes. We highly recommend to look at these SMART attributes first.

• Read Error Rate [Stores data related to the rate of hardware read errors that occurred when reading data from a disk surface]
• Reallocated Sector Count [When the hard drive finds a read/write/verification error, it marks this sector as "reallocated" and transfers data to a special reserved area (spare area).]
• Spin Retry Count [stores a total count of the spin start attempts to reach the fully operational speed.]
• End to End Error [after transferring through the cache RAM data buffer the parity data between the host and the hard drive did not match]
• Command Timeout [The count of aborted operations due to HDD timeout]
• Reallocation Event Count [Count of sector remap operations]
• Current Pending Sector Count [Count of "unstable" sectors (waiting to be remapped, because of read errors). ]
• Uncorrectable Sector Count [The total count of uncorrectable errors when reading/writing a sector.]
• Soft Read Error Rate [Count of off-track errors.]

You can see that most of this attributes counts errors reading or writing sectors on the hard drive surface. If the attribute values rise (reach threshold), make a backup and change the hard drive.
For more information we recommend Wikipedias article.