The second part of the question is simple and factual:
Signing is when the executive (President, Prime Minister, or their appointed minister) indicate the country's willingness to agree to a treaty. Typically at the end of a period of inter-governmental negotiation, the governments will sign the treaty.
But in many countries (particularly democratic ones) Parliament needs to give legal force to the treaty, because the executive can't create new laws without the approval of Parliament. So the Prime Minister presents the treaty to Parliament who then pass a law to put the treaty into effect. This is called ratifying the treaty.
In multigovernment treaties, there are often clauses that state that the treaty doesn't bind the signatories until a certain number have ratified the treaty.
As an example, President Clinton signed the Kyoto Protocol, but the US Congress (in particular the Senate) didn't ratify it (Clinton didn't even bother presenting it to the Senate as they had already voted 95-0 to oppose any treaty on Kyoto-like terms), so the Kyoto Protocol has no legal status in the USA.
In the case of the Biological weapons treaty, a distinction can be made between "ratifying" the treaty (following the negotiations in the early 1970s) and "acceding" to the treaty. The treaty now does not permit any modifications to be made for the convenience of a particular state. So any countries that didn't sign the treaty in 1973, cannot now negotiate modified terms. The must accede to the treaty as it stands.
The first question, the answer has to be more vague. Israel doesn't generally publish details of its WMD programme on the internet. But the only reason to sign an international treaty is because a government feels that the treaty is in its self-interest. Therefore we say that Israel doesn't feel that this treaty would (on balance) benefit Israel, the natural assumption is that Israel has, or has had, a clandestine biological weapons programme, which they have no intention of disclosing to UN inspectors. Or they do not want the precedent of signing one WMD treaty, since they will not sign other WMD treaties.
