Ah, the joys of scansion! My understanding of the subject is solid but very basic, so I'll give you what I know, in the hope that somebody else can elaborate.
The Caesura in Ancient Poetry
The basic unit of Latin poetry is the foot: iamb, trochee, dactyl, anapest, spondee, amphibrach. A line of dactylic hexameter is made up of six dactyls (a long syllable followed by two short syllables, marked –⏖), some of which can be replaced with spondees (two long syllables, marked – –). Take the first line of the Æneid:
– ⏑ ⏑ – ⏑ ⏑ – – – – – ⏑ ⏑ – –
Arma virumque cano, Troiæ qui primus ab oris
If you separate each foot, you come up with this:
– ⏑ ⏑/– ⏑ ⏑/– –/– – /– ⏑ ⏑ /– –
Arma virumque cano, Troiæ qui primus ab oris
If, as Wikipedia suggests, a caesura occurs when a word ending comes during a foot rather than at the end of one, then there are caesuras (marked ‖) in every foot of this line:
– ⏑ ‖⏑/– ⏑ ‖⏑/– ‖ –/– ‖ – / – ⏑ ‖⏑ /– –
Arma virumque cano, Troiæ qui primus ab oris
However, usually in Latin poetry when people talk about the caesura, they mean what's called the principal caesura, which comes either in the third or fourth foot. In this verse it comes in the third foot:
– ⏑ ⏑/– ⏑ ⏑ /–‖ –/– – / – ⏑ ⏑ /– –
Arma virumque cano, Troiæ qui primus ab oris
There are various rules (some of them slippery, some of them disputed) for whether the principal caesura usually goes in the third or fourth foot.
The other thing to know about caesuras is that they're called strong when they follow a long syllable and weak when they follow a short syllable. So in the line above, the caesura is strong. In the following line, the caesura is in the third foot and is weak:
— — / — ⏑ ⏑ /— ⏑‖ ⏑/—⏑ ⏑/— ⏑ ⏑/— —
Spargens humida mella soporiferumque papaver
(Virgil, Æneid, book 4)
The Caesura in Modern Poetry
In modern English poetry, the caesura is much, much easier to understand. It's just when you pause while reciting a verse, often (though not always) for punctuation:
It is for you we speak, ‖ not for ourselves:
(Shakespeare, The Winter's Tale)
So basically that's what that sentence from Wikipedia means. :)
Note
For the metrical symbols code block, Brill has this fine list.