Please also read the FAQ.

A weighting is the relative degree of importance you attach to an attribute. For example, we're rarely at home, so Neighbourhood is not of great importance to us. But we often need to pick-up milk or bread on our way home and so we've given Local Shops a higher weighting (30%) than Neighbourhood (20%). Transport is most important to us at 40%. (We don't have children so we don't have 'Schools' as an attribute.) The weighting of an individual attribute must be a number between 0 and 100% (or .00 and 1.00) and Annalisa ensures your set of weightings for all your Attributes adds to 100% (or 1.00), whether or not you have normalisation turned on in Settings. See What's normalisation?
A rating is the degree to which an attribute is present in an option, or how much an option meets the attribute (or, when the attribute is an outcome, the probability that the option will generate this outcome). For example, in the South where we currently live, the gardens are bigger than in the north, where space is at a premium. So we rate the South at 70% on this attribute, compared with 10% for the North.

A score is the outcome for each Option given the current ratings and weightings. It is arrived at by multiplying the Option's rating for each Attribute by the Weighting for that attribute and summing across all the attributes. In our example, the score shows us that the North is where we should live. The North did not rank highest in all attributes, but because we weighted the attribute where the north did badly as less important, it came out on top, with West next. The score of .61 for the North comes from:

Neighbourhood rated at 0.6 x weighting of 0.2 = .12
Garden rated at 0.1 x weighting of 0.1 = .01
Transport rated at 0.6 x weighting of 0.4 = .24
Shops rated at 0.8 x weighting of 0.3 = .24
Score   = .61
An option is a potential course of action, like 'move north' in our example. Generally speaking it is one of a set of things that you are judging, selecting from, or evaluating. Options may be policies, strategies, programs, projects, applicants, assignments, objects… in fact anything about which judgements or decisions need to be made and in which multiple considerations (attributes) are relevant.
An attribute is something to take into account when making a judgement or decision (i.e. selecting from a set of options). It may be called many other things depending on the context – a criterion, a consideration, a quality, a characteristic, an indicator, a factor – but in every case the task is to rate each option in relation to each attribute and then weigh each attribute in relation to the other attributes. If an attribute has 0 (zero) weight then it isn't really an attribute for this decision. (If you don't have, or plan to have, kids, then Schools will not be an attribute in your move decision, though it may be a highly weighted attribute for others). In some situations it may be a good idea (for transparency and flexibility) to include such an attribute and explicitly assign it zero weight.
Annalisa arrives at a score based on the relative importance assigned to each of the attributes and requires that their weights add up to 100 (percent) or 1 (decimal). You can choose to assign weights with normalisation turned on or off. If normalisation is on, your weights will always sum to 1 (decimal) or 100 (percent) and every time you change a weighting value all the other values will be changed proportionately to enforce this. If you turn normalisation off, you can assign any value within range to your attributes. Normalisation will still be used in calculating the scores behind the scenes, so turning normalisation off makes no difference to the algorithm used in Annalisa; it simply makes it easier for you to set individual weights by: (a) allowing all the bars to appear to add-up to a value less than or greater than 100 (percent) or 1 (decimal) and; (b) preventing the dynamic alteration to all other weights in the way mentioned above. For example you might prefer to enter 40, 20, 80, 60 as your percentage weights. These add to 200% but the resulting scores will be exactly the same because Annalisa will normalise them to 20, 10, 40, 30.